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Discrete Math and Analyzing Social Graphs
Week 2
Combinations with Repetitions

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Combinations with Repetitions

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Combinations with Repetitions

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Combinations with Repetitions

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1.

Question 1

We have 15 objects in our dataset and we want to categorise them into 4 different categories. Each object falls into exactly one category. We are interested in the sizes of the categories. How many possible distributions of sizes of our four categories we can obtain?

1 / 1 point

816

Correct

This is correct! Each objects picks one out of four categories. Since we are interested only in the sizes of categories, order does not matter. There are repetitions, since several videos might fall in the same category. Thus we are dealing with combinations of size 15 out of 4 options with repetitions. So the answer to the problem is ${15 + (4-1) \choose 4-1} = {18 \choose 3}$ .